construct a bound set of a real numbers with exactly three limit points

Question

koikkara · Answer

$\color{red}{~\star~``Welcome~to~Open~Study~!!"~\star~}$ > Let us consider a set, for example... $Y = {1/n : n∈N}U{1+1/n : n∈N}U{2+1/n : n∈N}$. Using these points, i considered $(2,3)U(1,2)~or~(1,2)U(2,3)$, as a set, Now, The set $Y = (1,2)U(2,3)$ has x as a limit point for any x in (1,2) since the closure of Y - {x}, which equals [1,3], contains x. So A has more than 3 limit points. $Ref:$ http://www.et.byu.edu/~vps/ET502WWW/EXERCISES/6-topology.pdf $Hope~it~helps~!!$ Don't Forget, $Appreciate~the~Best~Answer$ with a click on $\color{purple}{"Best Response"}$ Button Too ! $\color{darkgreen}{~''Nice~To~Meet~You~!!"}$ @sayeeda